Allele frequency spectrums (AFS) do not give a solid view of ancient bottlenecks, but they do of recent population structure. Ironically, very recent bottlenecks are not well ascertained by MSMC and PSMC and LD-Blocks, but they are clear in AFS. This is covered pretty well here:
So yes, in the ancient past you cannot really infer much from AFS, but that has never been @glipsnort’s claim. His claims are consistent with what I showed with argweaver.
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@glipsnort has not made any claims of heliocentric certainty.
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He would agree that past about 500 kya, we do not expect allele frequency spectrums to detect a bottleneck of a single couple. That is where he places a tentative cutoff. So his results are essentially the same as argweaver, though the evidence form argweaver is much stronger.
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His original reason for delving into AFS was to respond to some young earth creationists that claimed the AFS was inconsistent with a large ancient population and required a single couple origin just 6,000 years ago: (Can someone explain like I'm 5 yo, what's wrong with this refutation of Biologos?).
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His response to Ola Hossjer (colleague of @agauger) has been very well measured, and entirely correct. (Glipsnort responds to a critical article) Notice that he does not prese a case against ancient bottlenecks, but only for common ancestry with great apes and huamns, and against a recent bottleneck. Both those claims are very well supported by the evidence, and he produces analysis of his own all the time.
I know you are not attacking @glipsnort personally, or even leveling an unfair scientific critique. I do think, however, it is important to clarify that he has been a measured and careful voice. In my opinion, he has not drawn incorrect conclusions from the AFS work, nor has he overstated his certainty of those results.